void tisbod_c ( ConstSpiceChar * ref,
SpiceInt body,
SpiceDouble et,
SpiceDouble tsipm[6][6] )
Return a 6x6 matrix that transforms states in inertial coordinates to
states in body-equator-and-prime-meridian coordinates.
PCK
NAIF_IDS
ROTATION
TIME
None.
VARIABLE I/O DESCRIPTION
-------- --- --------------------------------------------------
ref I ID of inertial reference frame to transform from
body I ID code of body
et I Epoch of transformation
tsipm O Transformation (state), inertial to prime meridian
ref is the NAIF name for an inertial reference frame.
Acceptable names include:
Name Description
-------- --------------------------------
"J2000" Earth mean equator, dynamical
equinox of J2000
"B1950" Earth mean equator, dynamical
equinox of B1950
"FK4" Fundamental Catalog (4)
"DE-118" JPL Developmental Ephemeris (118)
"DE-96" JPL Developmental Ephemeris ( 96)
"DE-102" JPL Developmental Ephemeris (102)
"DE-108" JPL Developmental Ephemeris (108)
"DE-111" JPL Developmental Ephemeris (111)
"DE-114" JPL Developmental Ephemeris (114)
"DE-122" JPL Developmental Ephemeris (122)
"DE-125" JPL Developmental Ephemeris (125)
"DE-130" JPL Developmental Ephemeris (130)
"GALACTIC" Galactic System II
"DE-200" JPL Developmental Ephemeris (200)
"DE-202" JPL Developmental Ephemeris (202)
(See the routine chgirf_c for a full list of names.)
The output tipm will give the transformation
from this frame to the bodyfixed frame specified by
body at the epoch specified by et.
body is the integer ID code of the body for which the
state transformation matrix is requested. Bodies
are numbered according to the standard NAIF
numbering scheme. The numbering scheme is
explained in the NAIF_IDS required reading file.
et is the epoch at which the state transformation
matrix is requested. (This is typically the
epoch of observation minus the one-way light time
from the observer to the body at the epoch of
observation.)
tsipm is a 6x6 transformation matrix. It is used to
transform states from inertial coordinates to body
fixed (also called equator and prime meridian --- PM)
Given a state s in the inertial reference frame
specified by ref, the corresponding bodyfixed state
is given by the matrix vector product:
tsipm * s
The X axis of the PM system is directed to the
intersection of the equator and prime meridian.
The Z axis points along the spin axis and points
towards the same side of the invariable plane of
the solar system as does earth's north pole.
NOTE: The inverse of tsipm is NOT its transpose.
The matrix tsipm has the structure shown below:
- -
| : |
| r : 0 |
| ......:......|
| : |
| dr_dt : r |
| : |
- -
where r is a time varying rotation matrix and
dr_dt is its derivative. The inverse of this
matrix is:
- -
| T : |
| r : 0 |
| .......:.......|
| : |
| T : T |
| dr_dt : r |
| : |
- -
The CSPICE routine invstm_c is available for
producing this inverse.
None.
1) If the kernel pool does not contain all of the data required
for computing the transformation matrix, tsipm, the error
SPICE(INSUFFICIENTANGLES) is signalled.
2) If the reference frame ref is not recognized, a routine
called by tisbod_c will diagnose the condition and invoke the
SPICE error handling system.
3) If the specified ID code body is not recognized, the
error is diagnosed by a routine called by tisbod_c.
None.
The matrix for transforming inertial states to bodyfixed
states is the 6x6 matrix shown below as a block structured
matrix.
- -
| : |
| tipm : 0 |
| ......:......|
| : |
| dtipm : tipm |
| : |
- -
This can also be expressed in terms of Euler angles
phi, delta and w. The transformation from inertial to
bodyfixed coordinates is represented in the SPICE kernel
pool as:
tipm = [w] [delta] [phi]
3 1 3
Thus
dtipm = D[w] /Dt [delta] [phi]
3 1 3
+ [w] D[delta] /Dt [phi]
3 1 3
+ [w] [delta] D[phi] /Dt
3 1 3
If a binary PCK file record can be used for the time and
body requested, it will be used. The most recently loaded
binary PCK file has first priority, followed by previously
loaded binary PCK files in backward time order. If no
binary PCK file has been loaded, the text P_constants
kernel file is used.
If there is only text PCK kernel information, it is
expressed in terms of ra, dec and w (same w as above), where
ra = phi - pi/2
dec = pi/2 - delta
The angles ra, dec, and w are defined as follows in the
text PCK file:
2 ____
ra2*t \
ra = ra0 + ra1*t/T + ------ + / a sin theta
2 ---- i i
T i
2 ____
dec2*t \
dec = dec0 + dec1*t/T + ------- + / d cos theta
2 ---- i i
T i
2 ____
w2*t \
w = w0 + w1*t/d + ----- + / w sin theta
2 ---- i i
d i
where:
d = seconds/day
T = seconds/Julian century
a , d , and w arrays apply to satellites only.
i i i
theta = THETA0(i) + THETA1(i)*t/T are specific to each
i
planet.
These angles -- typically nodal rates -- vary in number and
definition from one planetary system to the next.
Thus
____
2*ra2*t \
dra/dt = ra1/T + ------- + / a THETA1(i)/T cos theta
2 ---- i i
T i
____
2*dec2*t \
ddec/dt = dec1/T + -------- - / d THETA1(i)/T sin theta
2 ---- i i
T i
____
2*w2*t \
dw/dt = w1/d + ------ + / w THETA1(i)/T cos theta
2 ---- i i
d i
Note that the data needed to compute the output state transition
matrix must have been made available to your program by having
loaded an appropriate binary or text PCK file via furnsh_c.
Example 1.
In the following code fragment, tisbod_c is used to transform
a state in J2000 inertial coordinates to a state in bodyfixed
coordinates.
The 6-vector eulang represents the inertial state (position and
velocity) of an object with respect to the center of the body
at time et.
#include "SpiceUsr.h"
.
.
.
/.
First load the kernel pool.
./
furnsh_c ( "planetary_constants.ker" );
/.
Next get the transformation and its derivative.
./
tisbod_c ( "J2000", body, et, tsipm );
/.
Convert position to bodyfixed coordinates.
./
mxvg_c ( tsipm, eulang, 6, 6, bdstat );
Example 2.
In the example below, tisbod_c is used to compute the angular
velocity vector (with respect to an inertial frame) of the
specified body at time et.
#include "SpiceUsr.h"
.
.
.
/.
First get the state transformation matrix.
./
tisbod_c ( body, et, tsipm );
/.
This matrix has the form:
- -
| : |
| tipm : 0 |
| ......:......|
| : |
| dtipm : tipm |
| : |
- -
We extract tipm and dtipm:
./
for ( i = 0; i<3; i++ )
{
for ( j = 0; j<3; j++ )
{
tipm [i][j] = tsipm[i ][j];
dtipm [i][j] = tsipm[i+3][j];
}
}
/.
The transposes of tipm and dtipm, (tpmi and dtpmi), give
the transformation from bodyfixed coordinates to inertial
coordinates and its time derivative.
Here is a fact about the relationship between angular
velocity associated with a time varying rotation matrix
that gives the orientation of a body with respect to
an inertial frame:
The angular velocity vector can be read from the off
diagonal components of the matrix product:
t
omega = dtpmi * tpmi
t
= dtipm * tipm
the components of the angular velocity v will appear
in this matrix as:
_ _
| |
| 0 -v(3) v(2) |
| |
| v(3) 0 -v(1) |
| |
| -v(2) v(1) 0 |
|_ _|
Pick off the angular velocity components from omega.
./
mtxm_c ( dtipm, tipm, omega );
v[0] = omega [2][1];
v[1] = omega [0][2];
v[2] = omega [1][0];
The kernel pool must be loaded with the appropriate coefficients
(from the P_constants kernel or binary PCK file) prior to calling
this routine.
None.
N. J. Bachman (JPL)
W. L. Taber (JPL)
K. S. Zukor (JPL)
-CSPICE Version 1.0.3, 16-JAN-2008 (EDW)
Corrected typos in header titles:
Detailed Input to Detailed_Input
Detailed Output to Detailed_Output
-CSPICE Version 1.0.2, 10-NOV-2006 (EDW)
Replace mention of ldpool_c and pcklof_c with furnsh_c.
Added Keywords and Parameters section headers.
Reordered section headers.
-CSPICE Version 1.0.1, 02-JUL-2003 (EDW)
Corrected trivial typo in the Version 1.0.0 line.
The typo caused an integrity check script to fail.
-CSPICE Version 1.0.0, 20-JUN-1999 (NJB) (WLT) (KSZ)
Initial release, based on SPICELIB Version 3.3.0, 29-MAR-1995
transformation from inertial state to bodyfixed
Link to routine tisbod_c source file tisbod_c.c
|